Answer:-
7.23 x 10^8 yr
Explanation: -
According to the question
The half life of uranium t ½ = 4.5 x 10^9 yr
Disintegration constant k =0.693 / t ½
= 0.693 / 4.5 x 10^9 yr
= 0.154 x 10^-9 yr
Let us assume there is 1 mg of Uranium present currently
Current uranium C = 1 mg
Original Uranium present O = Currently present + Transformed into lead
= 1 mg + (238 / 206) x 0.102 mg
= 1 + 0.118
=1.118 mg
Time taken =(1 / k) ln ( O/ C)
= (1 / 0.154 x 10^-9 yr) ln (1.118mg / 1 mg)
= 7.23 x 10^8 yr
